That's a very simple model.
It assumes you only have 2 genes for colour, one from each parent. These are usually written as B for brown and b for blue.
B is dominant so if you have the genese Bb you will have brown eyes but you can pass on the b to your child. So if your brown eyed partner has Bb you can easily have a blue eyed child.
BUT there isn't just one gene for eye colour, instead of having BB, Bb, bb, or bB it's more like BbbBBbbB so there are many more possible combinations and this is where the green, grey and hazel.
So your eyes are a mix of colours but you only see the dominant one(s).
Think of it as looking through 8 pieces of glass on top of each other, if they are all blue then you will see blue, if a majority are brown you will see brown but with different combinations you might see gray, green, light blue, dark blue etc.
Added to the genetics are some genetic conditions, Waardenburg syndrome causes at least one blue eye, deafness and often white hair at the forelock.
This happens regardless of your family eye colour(s) so you get black people with bright blue eyes if they have Waardenburg.
https://www.thetech.org/ask-a-geneticist/articles/2004/ask2/
https://medlineplus.gov/genetics/understanding/traits/eyecolor/